Contact effects on the magnetoresistance of finite semiconductors

We propose a new theoretical method to study galvanomagnetic effects in bounded semiconductors. The general idea of this method is as follows. We consider the electron temperature distribution and the electric potential as consisting of two terms, one of which represents the regular solution of the energy balance equation obtained from the Boltzmann transport equation at steady-state conditions and the Maxwell equation, while the other is the effect of the specimen size that is significant near the contacts (the boundary layer function). With the distribution of the electric potential at the contacts and the electron temperature distribution at the surface of the sample taken into account, we find that the magnetoresistance is different from the one in the standard theory of galvanomagnetic effects in boundless media. We show that, besides the usual quadratic dependence on the applied magnetic field B, the magnetoresistance can exhibit a linear dependence on B under certain conditions. We obtain new formulas for the linear and quadratic terms of the magnetoresistance in bounded semiconductors. This linear contribution of the magnetic field to the magnetoresistance is essentially due to the spatial dependence of the potential at the electric contacts. We also discuss the possibility of obtaining the distribution of the electric potential at the contacts from standard magnetoresistance experiments. Because the applied magnetic field acts differently on carriers with different mobilities, a redistribution of the electron energy occurs in the sample and thus, the Ettingshausen effect on the magnetoresistance must be considered in bounded semiconductors.